In this section, we briefly review the best Bayesian based receiver in the literature, Expectation Propagation (EP) receivers [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, which is a combination of Bayesian and MMSE concepts.
The main idea of the EP is to iteratively approximate the distribution of a random transmitted symbol vector, \({\bf x}\)  by using a Gaussian probability distribution function (PDF) approximation based on the received signals \({\bf y}\) , \(p^{(t)}({\bf x}|{\bf y})\) , and a pair of tuning parameters, \(({\lambda }^{(t)},{\gamma }^{(t)})\)  which are obtained from the exponential family distributions [7]}. \( p^{(t)}({\bf x}|{\bf y})\)  is given as
\( p^{(t)}({\bf x}|{\bf y}) = \mathcal {N} \left({\bf x}, {{\mu }}^{(t)}_{\rm obs}; {\Sigma }^{(t)}_{\rm obs} \right)\) 
